Polar Equation To Rectangular Form

Catechumen Equation from Rectangular to Polar Class

Problems were equations in rectangular form are converted to polar course, using the relationship between polar and rectangular coordinates, are presented along with detailed solutions.
In what follows the polar coordinates of a point are (R , t) where R is the radial coordinate and t is the angular coordinate.
The relationships between the rectangualr (x,y) and polar (R,t) coordinates of a points are given by
R² = x² + y² y = R sin t x = R cos t

Problems on Converting Rectangualar Equations to polar form

Problem i

Convert the equation
2xⁱⁱ + 2y² - x + y = 0
to polar course. Solution to Problem 1

Let the states rewrite the equations as follows:
2 ( xⁱⁱ + y² ) - ten + y = 0

We at present use the formulas giving the relationship between polar and rectangular coordinates: R² = xⁱⁱ + y^two, y = R sin t and x = R cos t:
2 ( R² ) - R cos t + R sin t = 0
Factor out R
R ( 2 R - cos t + sin t ) = 0
The to a higher place equation gives:
R = 0
or
2 R - cos t + sin t = 0
The equation R = 0 is the pole. But the pole is included in the graph of the second equation 2 R - cos t + sin t = 0 (cheque that for t = π / 4 , R = 0). We therefore tin can proceed only the second equation.
ii R - cos t + sin t = 0
or
R = (1 / 2)(cos t - sin t)

Problem 2

Convert the equation
x + y = 0
to polar form.
Solution to Problem 2

Use y = R sin t and x = R cos t into the given equation:
x + y = 0
R cos t + R sin t = 0
Cistron out R
R ( cos t + sin t ) = 0
The higher up equation gives:
R = 0
or
cos t + sin t = 0
The equation R = 0 is the pole. But the pole is included in the graph of the second equation cos t + sin t = 0 since this equation is independent of R. We therefore keep only the second equation.
cos t + sin t = 0
The to a higher place equation may be written as.
tan t = - 1
Solve for t to obtain
t = 3 π / 4

All points of the grade (R , three π / four) are on the graph of the to a higher place equation. Information technology is the equation of a line in polar course.